One of the specific cases of feature learning mystery is MLP being able to learn sparse parities, i.e. output is XOR of some k bits of the input which is n bits in total, and MLP is able to learn this in close to O(n^k), which is actually the computational limit here. In this paper they give a very nice intuition (Section 4.1) about why even in a network with a single layer (and ReLU on top of it) gradients will contain some information about the solution. TLDR: Gradient of “ReLU of the sum of incoming activations”, if we consider incoming weights all being one (that’s the example they study), is just a majority function. And an interesting property of majority function is that contribution of k-wise feature interactions to it decays exponentially with k. And because of this decay gradients end up being informative.
There was also an interesting paper about limitations of gradient optimization, which I can’t find now. One of the examples there was a task which is basically a XOR of k simple image classification problems (something about detecting angle of a line from the image). And they show that without intermediate target (i.e. target for a single classification task instead of XOR of all of them) it stops learning around k=4, while with intermediate target it can go up to k=20. Which is to say that even in cases where there is a compact structure in the problem, neural networks (and maybe any gradient-based models) will not always be able to find it quickly.
That might indeed be one of the reasons, but also I think there is just not that much evidence of x-rationality actually helping in real world for most people? There are examples about bitcoin, covid and AI, but being able to be right about something once in a decade doesn’t seem like enough justification to read the Sequences
(For the record, I’ve read Sequences, and HPMOR and planecrash and CFAR Handbook)